This project will investigate theory, methods and applications of mathematical statistics and probability, with particular emphasis on the problems with data collected by NICHD. Current focus is on the analysis of data arising from longitudinal studies with repeated measurements. Examples of NICHD projects on longitudinal studies are Small-for-Gestational Age Study I and Study II in Alabama and Scandinavia, Maternally Linked Longitudinal Studies in Missouri and Utah, Preventing Problem Behavior Among Middle School Students and Longitudinal Study of Vaginal Flora. A host of statistical procedures for estimation and hypothesis testing will be proposed and investigated for the time varying coefficient models via their asymptotic properties and simulations. Applications will be developed to handle questions concerning various issues in perinatal and reproductive epidemiology. New and rigorous statistical methods and algorithms will be generated and validated through investigation of their statistical and probabilistic properties. Computer-intensive techniques such as bootstrapping methodology will be investigated for the relevant problems. Among the applications of the developed methodology are fetal growth, maternal risk factors and pregnancy outcomes. Studying the attachments between children and care providers shortly before political reunification of the city. Comparative analyses show that infants were more likely to establish secure attachments to their care providers after reunification than before perhaps because care providers in the later regime focused on the styles and needs of individual infants. In a subsequently study, researchers observed in detail the everyday experiences of toddlers who either did or did not receive regular out-of-home care. The data showed different diurnal patterns of adult attention, stimulation, and emotional exchange, although the total amount of social interaction experienced over the course of the day did not differ depending on whether or not the toddlers spents time in day care. In the Berlin longitudinal study, researchers are assessing the psychophysiological and behavioral tendencies of infants in order to assess the effects of prior individual differences in emotional reactivity and infant-mother attachment on the adaptation to out-of-home center care. Preliminary analyses indicate that the securely attached infants had slower and more variable heart rates at day care when their mothers were present than insecurely attached infants did. The quality of infant-careprovider relations, infant-parent attachment, and infant temperament may all shape adaptation to day care.